Needle Roller Bearings - Ntn-snr.com

Technical Data
NTN
11.3 Calculation Examples
11.3.1 Shrinkage factor and post-installation
clearance of drawn cup needle roller bearing
The recommended fit data for the standard bearings is
as described in Table 1 on page B-33. This paragraph
describes hereunder the calculation methods to be used
when the bearing fit conditions are reviewed in detail.
2) Inscribed circle diameter after complete bearing fit
in the housing on actual machine
[1] Inscribed circle diameter in press-fitting of master ring
T
1) Calculation of bearing shrinkage factor
For the drawn cup bearings, the shrinkage factor is
calculated using the following method.
H
Fig. 11.5
D
DH
Housing
de
Drawn cup bearing
1S 2
2t
0.7S 2 1.31t 2 0.71.3t 2 1S 2 11.1
E 2
E 1 E 2
Where,
Outer ring shrinkage factor
DH Housing outer diameter mm
dnom Nominal diameter of fitting portion mm
de Rolling surface diameter of outer ring mm
E Modulus of housing vertical elasticity
(Young’s modulus) MPa (kgfmm 2 )
E Modulus of outer ring vertical elasticity
(Young’s modulus)
2.0710 6 MPa (21 200kgfmm 2 )
dnom
S
DH
de
t
dnom
Fig. 11.4
dnom
H Housing inner diameter mm
T Roller diameter + plate thickness mm
D Outer diameter of drawn cup needle roller bearing mm
Li Post press-fit inscribed circle diameter mm
When the master ring is press-fitted, the dimension of
"roller diameter + plate thickness" remains unchanged.
Hence, the inscribed circle diameter Li is determined by
the following formula.
LiD2TDH1D2TH
(11.2)
Determine the mean value of "roller diameter + plate
thickness" (=T) and standard deviation from formula
(11.2). The mean value of formula (11.2) is determined
as follows.
mLi1mDm2TmH
Standard deviation of formula (11.2)
(11.3)
Li212D22T 22H 2 (11.4)
In the case of master ring, due to H 2=0 the formula
(11.4) is expressed as follows.
Li212D22T 2 (11.5)
The unknown values in formulas (11.3), (11.5) are only
mT and 2T 2 . Hence, substitute the known numerical
values for formulas (11.3), (11.5) to determine m2T and
2T 2 .
[2] Even when bearing ring is press-fitted in the housing
on actual machine, consider the inscribed circle
diameter similarly to the master ring press-fit.
Herein, the calculation formulas for press-fit in the
housing on actual machine can be discriminated as
follows from formula (11.3), (11.4) by adding " " to
each formula.
mLi1mDm2TmH (11.6)
Li212D22T 22H2 (11.7)
[3] For m2T and 2T 2 in formula (11.6), (11.7), substitute
the values determined previously for the respective
formula.
[4] From the calculations, the inscribed circle diameter in
press-fitting in the housing on actual machine can be
A-54